4/5*b-6=-9/10*b+2

Solution for 4/5*b-6=-9/10*b+2 equation:

4/5b-6=-9/10b+2

We move all terms to the left:

4/5b-6-(-9/10b+2)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 10b+2)!=0

b∈R


We get rid of parentheses

4/5b+9/10b-2-6=0

We calculate fractions


40b/50b^2+45b/50b^2-2-6=0

We add all the numbers together, and all the variables

40b/50b^2+45b/50b^2-8=0

We multiply all the terms by the denominator


40b+45b-8*50b^2=0

We add all the numbers together, and all the variables

85b-8*50b^2=0

Wy multiply elements

-400b^2+85b=0

a = -400; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-400)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-400}=\frac{-170}{-800}
=17/80
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-400}=\frac{0}{-800}
=0
$